1. Field of the Invention
The present invention relates to filter equipment such as a filter composed of discrete elements, a filter incorporated into a hybrid IC and a filter incorporated into a monolithic IC. More particularly, the present invention relates to a simple design method for a linear phased filter.
2. Description of the Related Art
Filter equipments are conventionally used in a wide range of electric apparatuses. A filter equipment is a device for filtering an input signal at a predetermined frequency. Some filters are composed of discrete elements, and others are incorporated into an IC such as a hybrid IC.
FIGS. 9 and 10 show examples of conventional filters. These filter equipments are designed in accordance with a technique of superimposing filters having a comparatively simple structure, namely, comparatively simple characteristics so as to synthesize a filter equipment having desired characteristics.
For example, the filter equipment shown in FIG. 9 is composed of bandpass filters (hereinunder referred to as "BPF") 2 and 6, and trap filters (hereinunder referred to as "TRAP") 4 and 8 which are connected in series in any given order. Such a filter is synthesized in accordance with the steps shown in FIGS. 11A to 11N.
The BPF 2, TRAP 4, BPF 6 and TRAP 8 have simple structures such as those shown in FIGS. 11A to 11D, respectively. Each of these filters as a constituent of the filter equipment is composed of an inductor (L), a capacitor (C) and the like. The BPF 2, TRAP 4, BPF 6 and TRAP 8 have gain responses shown in FIGS. 11E to 11H, respectively, and group delay responses shown in FIGS. 11I to 11L, respectively. In these drawings, the symbol f represents frequency, G gain and D delay.
By connecting these BPF 2, TRAP 4, BPF 6 and TRAP 8 in the form of a cascade, the gain response shown in FIG. 11M and the group delay response shown in FIG. 11N are obtained. In other words, FIGS. 11M and 11N show the gain response and the group delay response synthesized from the characteristics shown in FIGS. 11E to 11H and FIGS. 11I to 11L, respectively. If a signal is input from an input terminal 10 to the thus-synthesized filter equipment, a signal filtered in accordance with the characteristics shown in FIG. 11M and FIG. 11N is obtained from an output terminal 12.
The filter equipment shown in FIG. 10 is composed of a low-pass filter (hereinunder referred to as "LPF") 14, TRAP's 16, 20 and a high-pass filter (hereinunder referred to as "HPF") 18 which are connected in the form of a cascade. Each of the constituents LPF 14, TRAP 16, 20 and HPF 18 of this filter equipment also has a simple structure, which consists of L, C, etc.
The LPF 14, TRAP 16, HPF 20 and TRAP 18 have the structures shown in FIGS. 12A to 12D, respectively, and the gain responses and the group delay responses thereof are shown in FIGS. 12E to 12H, and 12I to 12L, respectively. Therefore, the gain response shown in FIG. 12M and the group delay response shown in FIG. 12N are realized by connecting the LPF 14, TRAP 16, HPF 20 and TRAP 18 in the form of a cascade. In this conventional filter equipment, if a signal is input from an input terminal 22 to the thus-synthesized filter equipment, a signal filtered in accordance with the characteristics shown in FIGS. 11M and 11N is obtained from an output terminal 24 in the same way as in the filter equipment shown in FIG. 9.
In this way, a conventional filter equipment having a given characteristic is realized by superimposing filters having a comparatively simple structure and a comparatively simple characteristic as the constituents thereof. According to this technique, design having a high degree of freedom is possible. For example, it is possible to realize a sharp cutoff characteristic by combining a cutoff through an LPF and a trap through a TRAP.
In the case of realizing a filter equipment in accordance with this technique, however, the generation of a ripple of the group delay is inevitable in the pass band. FIGS. 11N and 12N show that the group delay in the pass band d contains a ripple of m having a width of b. The width b of the ripple m becomes larger as the gain a is set at a larger value, as shown in FIGS. 11M and 12M.
Such inconvenience especially obstructs the realization of a linear phased filter. The linear phased filter refers to a filter having a linear phase characteristic in the pass band. Since the shape of the phase characteristic is equivalent to the shape of integrated group delay responses, a linear phased filter is not obtained unless the group delay response is flat. A linear phased filter is a filter required in, for example, acoustic apparatuses so as to faithfully reproduce the original sound.